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113-rosay-07spex02-key

# 113-rosay-07spex02-key - DM‘ go him(403:6 DM(\$600...

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Unformatted text preview: DM‘( go him (403:6): DM(\$600, 48.g°)g-3 X0: \$6oG-L‘g'ge Y's’ o, Ahﬁmfe‘r Q8123“ Wi’UlA alger Vdorl'dg * 0 Math 113 EXAME 2007, (1 hour and 15 minutes). Instructor: ' SECTION: NO CALCULATOR EXCEPT FOR PAGE 1. As usual7 all angles shown in triangles (Problems III, V, VI) are angles with measure in the range from 0° to 180°. There is no orientation of the angle. ' 1. Given sinzc —2, show all the possible terminal sides for the angle as (in standard position). Show the angle 2:0 such that sin 3:0 —%—, and 270° 5 3:0 S 450°. Using your calculator, give an approximate value of \$0. Give also an approximate value of the radian measure of the angle 9:0. . (25 points) 3' 2.403569. txAﬁx—~ bu; (360°+>K\. --\_—I [1 NmV, We wac It .— .— ant" Ti— H” \80 5'. 1,35“ nadiovwa. "ﬁllet: radxcwo‘ .n— —u Problems II-VI: NO CALCULATOR - N O CALCULATOR - NO CALCULATOR. IL Graph y 2 1 + tan(2x + Your graph should clearly show the vertical asymptotes and should show values of a: for_which y = l, and values of a: for which 3/ = 2. (25 points) . T l , ?ev\oa9~ .1: TE‘ ‘ I 2*+1L:;Tl; & X: 1; V , \$0 Wank “Val/“(A / ' I Maw‘plroli flax: 19' :1, III. 1) Give the exact value of cos 6 (use the triangle ABC). Low 0%(009M90 Li“: 51+19‘- 2(517} a» 9 9.01 The ‘. .Coo9=~——- W“ , 37 A5 2) Give the exact value of tan 0. i v- - \ l‘ "L : 2:“4 1 HM“ 9‘ @3749 ' (24» 3) Give the exact value of h. _ ‘ k _738L; Amé:~T 9 3° 10‘ II. Graph 3/ = 1 + tan(§ + g). Your graph should clearly Show the vertical asymptotes and should show values of a: for which y = l, and values of x for which y = 2. (25 points) Nix/cull]; 1 QTY. ‘ . l/l ; ‘E ‘11 31“ 1.... V \stzhlamgzl W L _\ l2. mT 7(ﬁ)2\&\fovn3.g 1 o - l ,1 _ ‘ YléngJe M“ l ' V I '\( [1W\:\/lo\: ‘2. I 111' ‘ I (30 pOinté) '_1) Give the exact value of c056 ( use the triangle ABC). > LOvarQ wm‘M/o 90¢: 51+ 61—- 2 (5x6)(,03 9 mmme C039: ‘7;- 2) Give the exact value of tan 6’. L ‘1 _ l 1 v- [5‘ _ 5—6 I+Vm~ 9‘ ably ) low 9.6? __l . \Ez km 9: E6— ~ m ) WQ‘QAQW Oﬁé Qé 5‘00 ) meva%\x ' vs ’ :3 [ell/(en Och/kw: M02 blhrL-i—Ccroq‘:\ M9 ) Wm l/WQ: W 3) Give the exact value of h. _\2Wl Amati?" JR" \3 3 IV. Given cos oz = cos ﬂ = Give all the possible values of eos(a +48). Show by examples that all these values are indeed possible. ' I (30 points) L Mu map: (J; “3%: i: (+ % \oablA Ivaol mmuxew mlgbonh Au:& Malena: [54 0 ) 3-2. odneAM/Ca—Q» I " L‘ Cong; He) : (we? Gel,” .— V. ‘ - _ , (25 points) - 1) Let :1: and y be such as tanﬁv + y) = 2133mm. Show that tany = tanzc — 2tan2 a: tan y. j—YmXVMV 47% 7~+VM\I: Q.wa ( (_\~aM)¢VM\/) =>' \‘m‘lerVw/‘Y: (LVW‘F— :> Wm» \1 -: Jhw >< — LVwAix \rmx/ Figure for questions 2 and 3 of Problem V: - \9 c \ -. 1c D I : 11 2) Show that, tan(x + y) = 2 tan 2:, and that sin y = sin :c sin 6. .‘BD‘ » 112‘ [v"z*-NV*“WV6€X>. )6 (M73: : K M W» \m “WEB ﬁrﬁf \WAX 1». 16W - 3... (MW/wwﬂ Amyso ka+1yzszx mm ” \on Lmohcwawwgwgk ACE ‘21:?“ z 40“ gobx‘n)’:—ﬂ—~bwe : JaOuXAWB ) (AC1 _ _ Q‘ (MVn/Cwﬁeik ADCB‘ \geccwoc 19w x 2 [AU Prove that y < 3:. Scmc Mm] 1mm AM‘AQ awA 2m (9 <\ ) AV; \/ 4 wa (an (“mm M WSW) . T‘Mém V4 x ( annual)» _ 0M9, CAM abowe MAM] < km X ’9me \‘ow \/ : \‘mw—ZM‘AH \PM\/ E acamJu‘vn/a \73 0 “MA 2-)\ 5 “059\$ ‘100 mm)‘ (Dig-95400 90 . VI. (25 points) onquNVx‘co Cw29)c,[email protected]‘gv3\ (h‘fmmél owe?!)a ' )NM) —-"",_.__._ 1) Evaluate @(29) L05 ‘2 Q :_ g 9313 u; WWB/QVVWKMVXA chw D 2) Give the exact value of cos 6, sin6 and tan 6. \+C.m>2.Q'I-Q-.Ce’>29 CKCVJSM. IC 3, B "L , Q. CooLC922: ,bw19:\_u’>9'”—7° 7 9 \[Z A \l‘mig: AW " go CQD (97- % J bwe (I! ) (Jog V? 3) Give the EXACT values of lAD| and lDCl. g 3 ﬂ Cb @ 3 [(M‘W vm\m\62A QBD))DO C‘: - \f—j: \$501M Pmpgamﬁmmw m at, \Ac\”‘_ gm: we sgAek 4mm \(59\: 99m» 9 (MW/WW6“ “393200 i993 — 1F; \A©\: IR B\—\ED\: 9.6-0-3? ...
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